Statistics Questions

Watching TV The 2012 general Social Survey asked a large number of people how much time they spent watching TV each day The mean number of hours was 3 09 with a standard deviation of 2 86 Assume that in a sample of 36 teenagers the sample standard deviation of daily TV time is 4 2 hours and that the population of TV watching times is normally distributed Can you conclude that the population standard deviation of TV watching times for teenagers is greater than 2 86 Use the a 0 01 level of significance Part 0 5 Part 1 of 5 State the appropriate null and alternate hypotheses Ho Choose one H 0 Choose one This hypothesis test is a ch X Espa o 6 V B

Babies A sample of 25 one year old girls had a mean weight of 24 1 pounds with a standard deviation of 4 3 pounds Assume that the population of weights is normally distributed A pediatrician claims that the standard deviation of the weights of one year old girls is greater than 3 pounds Do the data provide convincing evidence that the pediatrician s claim is true Use the a 0 05 level of significance Part 0 5 Part 1 of 5 State the appropriate null and alternate hypotheses H Choose one H 0 Choose one This hypothesis test is a Choose one test X 5 0

Lopez Young a research firm for the real estate industry studied the relation between z annual income in thousands of dollars and y sale price of house purchased in thousands of dollars A random sample of data was collected from mortgage applications for home sales in the region of the study and is given in the table Annual Income 81 136 59 143 53 93 123 100 108 This indicates House Price 161 9 201 4 Correlation coefficient 140 8 252 1 Conduct a linear regression Use the results to answer the following questions a What is the value of the correlation coefficient round to 3 decimal places What does the value tell you about the linear relationship between the annual income and the price of house purchased 111 7 145 5 317 5 198 271 2

A certain insecticide kills 50 of all insects in laboratory experiments A sample of 13 insects is exposed to the insecticide in a particular experiment What is the probability that exactly 5 insects will die Round your answer to fou decimal places

Calculate the range population variance and population standard deviation for the following data set If necessary round to one more decimal place than the largest number of decimal places given in the data 3 4 5 6 7 8 9 10 11 12 AnswerHow to enter your answer opens in new window 2 Points Range Population Variance Copy Data Keypad Keyboard Shortc

The FBI wants to determine the effectiveness of their 10 Most Wanted list To do so they need to find out the fraction of people who appear on the list that are actually caught Step 1 of 2 Suppose a sample of 1291 suspected criminals is drawn Of these people 361 were captured Using the data estimate the proportion of people who were caught after being on the 10 Most Wanted list Enter your answer as a fraction or a decimal number rounded to three decimal places

An economist wants to estimate the mean per capita income in thousands of dollars for a major city in California Suppose that the mean income is found to be 22 7 for a random sample of 183 people Assume the population standard deviation is known to be 6 3 Construct the 85 confidence interval for the mean per capita income in thousands of dollars Round your answers to one decimal place nswerHow to enter your answer opens in new window 2 Points Keyp Keyboard Shor

The mean points obtained in an aptitude examination is 103 points with a variance of 169 What is the probability that the mean of the sample would differ from the population mean by less than 2 8 points 63 exams are sampled Round your answer to four decimal places

Find the value of z such that 0 03 of the area lies to the right of z Round your answer to two decimal places Answer 2 Points Keypa Keyboard Shortc If you would like to look up the value in a table select the table you want to view then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using t Space key Note Selecting a cell will return the value associated with the column and row headers for that cell Normal Table 0 to z

For the given scenario determine the type of error that was made if any Hint Begin by determining the null and alternative hypotheses A software company states 10 as the improvement in students grades after using the software One student claims that the improvement in students grades after using the software is different from 10 The student conducts a hypothesis test and fails to reject the null hypothesis Assume that in reality the improvement in students grades after using the software is 15 Was an error made If so what type Answer 2 Points O No correct decision O Yes Type Il error Yes Type I error k Keyboard S

dicate the level of measurement for the data set described wer 2 Points Satisfaction ratings from course surveys given at the end of the semester Nominal O Interval Ratio Ordinal Ke

An eight sided die which may or may not be a fair di has four colors on it you have been tossing the die for an hou and have recorded the color rolled for each toss What is the probability you will roll a purple on your next toss of the die Express your answer as a simplified fraction or a decimal rounded to four decimal places pink 42 yellow 51 purple 43 red 38

When an anthropologist finds skeletal remains they need to figure out the height of the person The height of a person in cm and the length of their metacarpal bone 1 in mm were collected and are in the table Find the correlation coefficient and coefficient of determination and then interpret both Data of Metacarpal versus Height Height of Person cm Length of Metacarpal mm 47 43 51 50 39 46 40 44 48 180 172 184 180 154 170 156 169 178 The correlation coefficient is r Select an answerv Select an answer correlation The coefficient of determination is r round to five decimal places which is a round to four decimal places so of the variability in the height of a person is explained by the length of

Consider the following box plots for Data Set A and Data Set B 45 80 45 48 Answer 2 Points 50 50 53 55 55 57 58 60 60 65 Step 1 of 2 Which data set has the largest value 65 67 66 Data Set A 70 74 70 75 Data Set B 75 80 80 83 85 85 85 90 90 94 95 8 95 00 F Kel

The following bar graph shows the per capita personal incomes for six states in 2003 Use this bar graph to answer th questions Income in Dollars 40 000 32 000 24 000 16 000 8000 0 T Per Capita Personal Income by State for 2003 33332 26838 Washington Arizona 28783 Indiana State 24977 Utah 26252 Kentucky 28235 North Carolina

Assume the random variable has a binomial distribution with the given probability of obtaining a success Find the following probability given the number of trials and the probability of obtaining a success Round your answer to fou decimal places P X 5 n 8 p 0 4

ye colors are an example of which type of data nswer 2 Points O Quantitative O Parameter O Inferential

1 Which of the following histograms shows the relative frequencies for the data in the table A Number Greater A Number Greater A Number Greater A Number Greater Than or Equal To Than or Equal To 1 and Less Than 2 6 0 and Less Than 1 18 Than or Equal To 2 and Less Than 3 4 Than or Equal To 3 and Less Than 4 2 0 60 0 07 X Frequency P X 0 20 0 13

4 At the local movie theater entrance group sizes were observed and recorded to better understand the social aspects of moviegoing The findings are in the data below Group Size X 12345 Frequency 2 47 24 198 Relative Frequency 0 02 0 47 0 24 0 19 0 08 Which table correctly displays the cumulative relative frequencies of group size

Suppose the probability of success in a geometric distribution is 0 25 What is the expected value 00 01 02 5 04

The table below represents a manufacturer s estimates for the sales of its product for the coming year What is the expected value O 500 O 1 550 502 150 Units sold 300 500 750 P sales 0 39 0 29 0 32

A patient with cancer undergoes treatment that has an expected value of a 90 reduction in tumor size The patient s tumor is 100 mm wide Which statement is correct O The patient s tumor will be 10 mm wide at the end of treatment O The patient s tumor will be gone at the end of treatment The patient s tumor will be smaller at the end of treatment O The patient s tumor has a 90 chance of being gone at the end of treatment The patient s tumor will most likely decrease by the end of treatment

8 1 Determine g for the area shown in Figure P8 1 y 2 2 1 2 4 4

3 Rowen conducts a survey to record the number of movies bought by each customer during a weeklong sale at his store Number of Movies X Frequency 1 25 2 40 35 45 3 4 S 6 20 15 7 Rowen calculates the relative frequencies and rounds to the nearest whole percent Which of the following is the correct cumulative relative frequency graph for Rowen s data

Ea time one part is randomly selected from a large group of mechanical parts The group contains five types of parts with lengths of 2 cm 3 cm 5 cm 7 cm and 8 cm The probability that a part is selected is proportional to its length A List all possible outcomes treat each length as one outcome and find the probability of eac of them The possible outcomes form a random variable X B Is X continuous or discrete C What is the probability that a randomly selected part has a length of 5 cm or less D What is the probability that a randomly selected part has a length greater than 3 cm

An engineer designed the following system to deliver signals from the 1 end to the 2 end The system contains 13 components all used for signal delivery As long as the signal can reach the 2 end the system is functional Assume that all components function independently The probability that each component is functional is listed in the table below Compute the probability that the system is functional A B 4 0 JET Component functioning 0 98 0 96 0 88 0 92 0 94 0 85 0 97 0 90 0 89 0 83 0 94 0 91 0 86 A B C D E F G H I Probability of K L M K 2

Ho 51 2 H 51 2 Your sample consists of 29 subjects with a mean of 49 2 and standard deviation of 4 18 Calculate the test statistic rounded to 2 decimal places

restaurant chain receives on average 24 pounds of meat on a daily basis The district manager of the restaurant chain decides to randomly sample 41 shipments from the company and finds a mean weight of 22 5 pounds with a standard deviation of 3 8 pounds Test at a 3 level of significance to determine whether or not the food distribution company sends less than they claim a Check all of the requirements that are satisfied random OF Ho the distribution is normal since 30 the distribution is normal since the a distribution is normal b Identify the null and alternative hypotheses 24 the distribution is normal since rup 10 and ng 10 H 24 OB c What type of hypothesis test should you conduct teft right or two tailed left tailed Oright tailed twe taited d Identify the appropriate significance level Make sure to enter your answer as a decimal

level of a 0 002 Ho 51 2 51 2 Ha You believe the population is normally distributed but you do not know the standard deviation You obtain a sample of size n 18 with mean M 44 5 and a standard deviation of SD 8 3 What is the test statistic for this sample Report answer accurate to three decimal places test statistic 3 425 OF What is the p value for this sample Report answer accurate to four decimal places p value 0 074

Consider the following table of data Complete parts a though c below X y 1 2 3 0 98 1 05 0 95 4 1 04 a Calculate the correlation coefficient ror decimal rounded to four decimal places as needed

The Turners have purchased a house for 130 000 They made an initial down payment of 30 000 and secured a mortgage with interest charged at the rate of 9 year compounded monthly on the unpaid balance The loan is to b amortized over 30 yr Round your answers to the nearest cent a What monthly payment will the Turners be required to make b How much total interest will they pay on the loan c What will be their equity after 10 years d What will be their equity after 22 years

Which of the statements is not true about continuous probability distributions O The total area under the density curve must be exactly 1 OIX is a continuous random variable taking values between 0 and 500 then P X 200 P X 200 O There are no disjoint events in continuous probability models O The probability of any event is the area under the density curve over the range of values that make up the event

company claims that a fast food restaurant chain receives on average 24 pounds of meat on a daily basis The district manager of the restaurant chain decides to randomly sample 41 shipments from the company and finds a mean weight of 22 5 pounds with a standard deviation of 3 8 pounds Test at a 3 level of significance to determine whether or not the food distribution company sends less than they claim a Check all of the requirements that are satisfied random the distribution is normal since n 30 the distribution is normal since the a distribution is normal the distribution is normal since np 10 and nq 10 b Identify the null and alternative hypotheses Ho Select an answer 000 0 H Select an answer c What type of hypothesis test should you conduct left right or two tailed left tailed right tailed two tailed d Identify the appropriate significance level Make sure to enter your answer as a decimal 0 e Which calculator function should you use Select an answer f Find the test statistic Write the result below and be sure to round your final answer to two decimal places g Find the p value Enter your answer as a decimal not a percentage and round to 4 decimal places

mm missing probabilities Start 04 Check Clear Help E E Now we can use the tree above answer the original question If Hugo or any other player for that matter tests positive what is the probability that he uses steroi Answer P FE Check Clear Help I give up

ow pretend you are tossing a coin 11 times and take X to be the total number of heads that come up There are then 2 1 2 048 possible outcomes HHHHHHHHHHH HHHHHHHHHHT HHHHHHHHHTH HHHHHHHHTHH HHHHHHHTHHH HHHHHHTHHHH HHHHHTHHHHH HHHHTHHHHHH HHHTHHHHHHH HHTHHHHHHHH HTHHHHHHHHH THHHHHHHHHH HTTTTTTTTTT THTTTTTTTTT TTHTTTTTTTT TTTHTTTTTTT TTTTHTTTTTT TTTTTHTTTTT TTTTTTHTTTT TTTTTTTHTTT TTTTTTTTHTT TTTTTTTTTHT TTTTTTTTTTH TTTTTTTTTTT Take X to be the total number of heads that come up The possible values of X are Separate the values with commas Now fill in the missing probabilities The other missing probabilities will appear when you correctly answer the question or press Do it x P X x 0 1 Check Clear Do it 2 3 4 5 6 7 8 9 10 11

nd the percentage of the total area under the standard normal curve between the following z scores z 1 40 and z 2 83

The number of on line Monday stock trades at OHaganStockTrades com a subsidiary of oHaganBooks com was measured for 50 Mondays in a row with the following results Stock trades 0 99 100 199 200 299 300 399 400 499 Number of Mondays 6 12 14 10 8 Thus for example there were between 300 and 399 trades on 10 of the 50 Mondays The measurement classes are the ranges 0 99 100 299 etc We would like X to measure the number of stock trades on a randomly selected Monday and then calculate its probability distribution Since we only have information for ranges of values we replace each measurement class by its rounded midpoint Let us take them one by one The midpoint of the 0 99 range is 0 99 59 5 which we round to 50 2 100 199 The midpoint of the 100 199 range is 2 Now continue in the same way to obtain the remaining values of X QUIZ 149 5 which we round to 150 Stock trades 50 Number of Mondays 6 Now use the above frequency table to complete the estimated probability distribution of X 150 12 250 14 350 10 450 8

Roll a pair of dice until you get a double 1 X the number of times you roll the dic Finite Type Infinite discrete Continuous Survey the entire population of the earth Y the average weight O Finite Type Infinite discrete Continuous Weigh yourself on some alien planet Z your exact weight in pounds O Finite Type Infinite discrete O Continuous Survey the entire population of the earth W Finite Type Infinito digorato H the total size of the population Check Check Check Check

A survey of randomly selected shopping malls yields the following data on the number of movie screens they contain 1 3 0 3 3 4 Movie screens Number of malls x Take X to be the number of movie screens in a selected mall so the values of X are given in the top row of the chart The frequencies are then the numbers in the second row For instance we observed X 0 no movie screens a total of 3 times as 3 of the malls had no movie screens So we rewrite the table as follows P X x 0 1 X 2 Check Clear 0 3 3 The experiment was performed a total of times Check Clear I give up To obtain the probability distribution divide each frequency by the total number of times the experiment was performed Do it 1 3 Frequency Think of the survey as repetitions of an experiment in which a mall is selected at random without replacement and the value of X is measured the number of screens 4 2 4 2 4 5 3 4 4 3 4 3 5 3 5 3

The mean miles per gallon of gas for a 2023 sedan is 67 mpg miles per gallon This distance is normally distributed with a sample standard deviation of 4 miles per gallon A newer engine model is suspected to improve miles per gallon A test is conducted where a sedan with the newer engine and 1 gallon of gas drives 30 times with a mean of 72 mpg Using an alpha of 0 02 conduct a hypothesis test to determine if the newer engine model improved the miles per gallon of the sedan Then interpret the decision within the context of the problem

MODELING REAL LIFE In a survey of 920 U S teenagers 81 said that helping others who are in need will be very important to them as adults The margin of error is 3 3 a Give an interval that is likely to contain the exact percentage of all U S teenagers who think that helping others who are in need will be very important to them as adults Between and b The population of teenagers in the U S is about 21 05 million Estimate the number of teenagers in the U S who think helping others will be very important to them as adults Between about million and million

The mean SAT score in mathematics is 532 The standard deviation of these scores is 36 A special preparation course claims that the mean SAT score of its graduates is greater than 532 An independent researcher tests this by taking a random sample of 9 students who completed the course the mean SAT score in mathematics for the sample was 563 Assume that the population is normally distributed At the 0 05 level of significance can we conclude that the population mean SAT score for graduates of the course is greater than 532 Assume that the population standard deviation of the scores of course graduates is also 36 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your responses as specified below If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the critical value Round to three or more decimal places 0 e Can we support the preparation course s claim that the population mean SAT score of its graduates is greater than 532 OYes No 1 X X O S OSO 0 0 P Q S 00 020 0 0

testers are streaming videos on the phones continuously The manufacturer claims that the population mean of the battery lifetimes of all phones of their latest model is 5 13 hours As a researcher for a consumer information service you want to test that claim To do so you select a random sample of 45 cell phones of the manufacturer s latest model and record their battery lifetimes Assume it is known that the population standard deviation of the battery lifetimes for that cell phone model is 2 42 hours Based on your sample follow the steps below to construct a 90 confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer s latest model Then state whether the confidence interval you construct contradicts the manufacturer s claim If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 45 phones of the manufacturer s latest model Take Sample Sample size 0 Point estimate 0 Population standard deviation 1 Critical value 0 Compute 0 00 Number of phones 45 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute H 0 00 Sample mean 2 00 5 36 4 00 Sample standard Standard error Margin of error 90 confidence interval deviation 90 confidence interval b Based on your sample graph the 90 confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer s latest model 5 00 2 02 Enter the lower and upper limits on the graph to show your confidence interval For the point enter the manufacturer s claim of 5 13 hours 6 00 Population standard deviation 2 42 8 00 X Critical values 0 005 2 576 0 010 2 326 20 025 1 960 0 050 1 645 20 100 1 282 10 00 10 00 a BIRO M

ounces of coffee per cup In a test of the machine the discharge amounts in 16 randomly chosen cups of coffee from the machine were recorded The sample mean and sample standard deviation were 5 92 fluid ounces and 0 13 fluid ounces respectively If we assume that the discharge amounts are approximately normally distributed is there enough evidence to conclude that the population mean discharge differs from 6 fluid ounces Use the 0 10 level of significance Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H HO H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the two critical values Round to three or more decimal places and e Can we conclude that the mean discharge differs from 6 fluid ounces OYes O No X 5 0 0 X O S OSO 0 0 P P S 00 020 O

2 Mr Acosta a market researcher is doing a study to see if there is a relationship between the age of a young adult 18 to 35 years old and the type of movie preferred A random sample of 93 adults revealed the following data Test if age and movie preferred are independent at the 05 level Movie Type Drama Science Fiction Comedy Totals Person s Age 18 23 yr 24 29 yr 30 35 yr 10 15 11 12 11 8 9 8 16 31 34 35 Totals 36 31 33 100

Based on the data shown below calculate the correlation coefficient rounded to three decimal places X 1 2 3 4 5 6 7 8 y 11 85 16 1 19 65 20 2 23 25 27 9 28 85 31 7

annually in its leased cars is 13 520 miles with a standard deviation of 1820 miles The company recently starting using new contracts which require customers to have the cars serviced at their own expense The company s owner believes the mean number of miles driven annually under the new contracts is less than 13 520 miles He takes a random sample of 14 cars under the new contracts The cars in the sample had a mean of 13 006 annual miles driven Assume that the population is normally distributed Is there support for the claim at the 0 10 level of significance that the population mean number of miles driven annually by cars under the new contracts is less than 13 520 miles Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your responses as specified below If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the critical value Round to three or more decimal places 0 e Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 13 520 miles OYes No H XI a S 0 0 Oso X 0 P Q 010 020 O O

patients To do so you select a random sample of 32 heart valve surgery patients and you record the surgery duration for each Assume it is known that the population standard deviation of the durations of all heart valve surgeries is 1 92 hours Based on your sample follow the steps below to construct a 99 confidence interval for the population mean of the surgery durations for all heart valve patients If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 32 heart valve patients Take Sample Sample size 0 Point estimate Population standard deviation Critical value 0 Compute 0 00 0 00 Number of patients 32 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 99 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 2 00 Sample mean 4 81 Standard error 4 00 Margin of error Sample standard 99 confidence interval 99 confidence interval deviation 1 21 6 00 X Confidence level 99 b Based on your sample enter the lower and upper limits to graph the 99 confidence interval for the population mean of the surgery durations for all heart valve patients 95 90 Population standard deviation 1 92 8 00 Critical value 20 005 2 576 20 025 1 960 20 050 1 645 10 00 10 00

nearest polling station Assume that the population of all such distances for voters in Rising Falls County is approximately normally distributed An article for the newspaper Keeping It Political claimed that the mean of this population is 6 45 km You want to test this claim so you select a random sample of 22 Rising Falls County voters and for each you record the distance the voter lives from their nearest polling station Follow the steps below to construct a 90 confidence interval for the population mean of all the distances voters in Rising Falls County live from their nearest polling station Then state whether the confidence interval you construct contradicts the reporter s claim If necessary consult a list of formulas a Click on Take Sample to see the results for your random sample Take Sample Sample size 0 Point estimate Sample standard deviation 0 Critical value 0 Compute Enter the values of the sample size the point estimate of the mean the sample standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 0 000 Number of people 0 000 22 2 000 Sample mean 4 795 Standard error 4 000 Margin of error 90 confidence interval b Based on your sample graph the 90 confidence interval for the population mean of all the distances the voters in Rising Falls County live from their nearest polling station Enter the values for the lower and upper limits on the graph to show your confidence interval For the point enter the claim 6 45 from the article 90 confidence interval 5 000 Sample standard deviation 2 312 6 000 X 8 000 Critical values 0 005 2 831 0 010 2 518 0 025 2 080 0 050 1 721 10 100 1 323 10 000 10 000

Several gamers were asked if they liked playing real time strategy RTS or role playing RPG games The results of the survey are shown in the Venn Diagram below RPG 0 17 0 68 0 83 14 8 What is the probability that a randomly selected person from this survey does not like playing RPG games 0 57 6 RTS 18